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Batalov · 2014-08-01, 17:24

When I first looked at the factordb entry it still had a c650 cofactor. But I recently was ruminating about x^y+y^x and convinced myself that x=4 would be a "Sierpinski-like number" for it because the expression was never prime (y>1), algebraically. Well, it is not a "Sierpinski-like number" in spirit, really; there is no covering set.

So, I submitted the
2015^2+2*4^672+2*2015*2^672
2015^2+2*4^672-2*2015*2^672
factors; the DB usually does gcd, but it didn't. Then I ran gcd in Pari and submitted the c245 and c405, and the entry started to look like it does now.

For fun, I've done the same to
2015^4+4^1015
2015^4+4^2015
Of course, one can also generate a test file of these algebraic factorizations with awk or perl and submit it to the DB...

2014-08-01, 17:24	#6
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 59×157 Posts	When I first looked at the factordb entry it still had a c650 cofactor. But I recently was ruminating about x^y+y^x and convinced myself that x=4 would be a "Sierpinski-like number" for it because the expression was never prime (y>1), algebraically. Well, it is not a "Sierpinski-like number" in spirit, really; there is no covering set. So, I submitted the 2015^2+24^672+220152^672 2015^2+24^672-220152^672 factors; the DB usually does gcd, but it didn't. Then I ran gcd in Pari and submitted the c245 and c405, and the entry started to look like it does now. For fun, I've done the same to 2015^4+4^1015 2015^4+4^2015 Of course, one can also generate a test file of these algebraic factorizations with awk or perl and submit it to the DB...